Related papers: Twisted vertex representations via spin groups and…

We give a practical computer algebra implementation of the Covering Lemma for finite transformation semigroups. The lemma states that given a surjective relational morphism $(X,S)\twoheadrightarrow(Y,T)$, we can establish emulation by a…

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…

Let $K$ be a differential field over $\C$ with derivation $D$, $G$ a finite linear automorphism group over $K$ which preserves $D$, and $K^G$ the fixed point subfield of $K$ under the action of $G$. We show that every finite-dimensional…

We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any…

The twisted Drinfeld double (or quasi-quantum double) of a finite group with a 3-cocycle is identified with a certain twisted groupoid algebra. The groupoid is the loop (or inertia) groupoid of the original group and the twisting is shown…

Let $\Gamma$ denote a $Q$-polynomial distance-regular graph with vertex set $X$ and diameter $D$. Let $A$ denote the adjacency matrix of $\Gamma$. For a vertex $x\in X$ and for $0 \leq i \leq D$, let $E^*_i(x)$ denote the projection matrix…

A conjectural generalization of the McKay correspondence in terms of stringy invariants to arbitrary characteristic, including the wild case, was recently formulated by the author in the case where the given finite group linearly acts on an…

We extend the graphical calculus developed in the first part of this paper to the parametrising spaces of quantum vertex operators. This involves a graphical implementation of the dynamical twist functor, which is a strict monoidal functor…

We prove the equivalence of two hierarchies of soliton equations associated to a simply-laced finite Dynkin diagram. The first was defined by Kac and Wakimoto using the principal realization of the basic representations of the corresponding…

Let F be the usual real field. Let W be a symplectic vector space over F. It is known that there are two different Weil representations of a Meteplectic covering group $\widetilde{Sp}(W)$. By some twisted actions, we reorganize them into a…

String theory, specifically type-II superstring theory, can be formulated in any ten-dimensional signature. To facilitate the study of supergravity and superstring theories in this setting, we present a uniform construction of supersymmetry…

We consider wormhole solutions in $2+1$ Euclidean dimensions. A duality transformation is introduced to derive a new action from magnetic wormhole action of Gupta, Hughes, Preskill and Wise. The classical solution is presented. The vertex…

The correspondence between four-dimensional $\mathcal{N}=2$ superconformal field theories and vertex operator algebras, when applied to theories of class $\mathcal{S}$, leads to a rich family of VOAs that have been given the monicker chiral…

We define the concept of weak pseudotwistor for an algebra $(A, \mu)$ in a monoidal category $\mathcal{C}$, as a morphism $T:A\otimes A\rightarrow A\otimes A$ in $\mathcal{C}$, satisfying some axioms ensuring that $(A, \mu \circ T)$ is also…

A $GL_d$-pseudocharacter is a function from a group $\Gamma$ to a ring $k$ satisfying polynomial relations which make it "look like" the character of a representation. When $k$ is an algebraically closed field, Taylor proved that…

In this paper we continue the study of $Q$-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin $R$-matrix associated with the affine quantum algebra…

We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…

In this paper we consider the category of F^\sigma of finite-dimensional representations of a twisted loop algebra corresponding to a finite-dimensional Lie algebra with non-trivial diagram automorphism. Although F^\sigma is not semisimple,…

We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups.…

We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally…